Adaptive Alpha with Branch Pruning

Factory function that creates an adaptive alpha adjustment system supporting branch pruning. Unlike alpha_adaptive_tree, which pre-computes a fixed schedule, this version can recompute the schedule on a pruned subtree after each depth — giving more alpha to surviving branches when dead branches are removed.

Usage

alpha_adaptive_tree_pruned(node_dat, delta_hat, max_depth = NULL)

Arguments

node_dat

A data.frame or data.table with columns nodenum, parent, depth, and nodesize. Typically extracted from a find_blocks result. The root node must have parent = 0 and depth = 1.

delta_hat

Estimated standardized effect size (e.g., Cohen's d). Conservative (larger) values produce more stringent adjustment, which preserves the FWER guarantee.

max_depth

Maximum depth to compute. Defaults to the maximum depth present in node_dat.

Value

A list with three components:

alphafn

A function with the standard alphafn interface: function(pval, batch, nodesize, thealpha, thew0, depth). Looks up the current alpha schedule by depth.

update

A function function(pruned_node_dat, thealpha) that recomputes the alpha schedule on the given (pruned) tree. Called by find_blocks after each depth's testable decisions.

reset

A function function(thealpha) that restores the alpha schedule to the full (unpruned) tree. Called by find_blocks at the start of each run to ensure independence across simulation iterations.

Details

The FWER guarantee follows from the same telescoping-sum argument as alpha_adaptive_tree, applied to the surviving subtree at each depth. Pruning decisions at depth \(d\) depend only on tests at depths \(1, \ldots, d\), which are independent of tests at deeper levels (under data splitting or independent permutation tests), so the conditional FWER bound holds.

When find_blocks detects a list-valued alphafn, it extracts these three components and calls reset at the start of each run and update after each depth.

Examples

nd <- data.frame(
  nodenum  = 1:7,
  parent   = c(0, 1, 1, 2, 2, 3, 3),
  depth    = c(1, 2, 2, 3, 3, 3, 3),
  nodesize = c(500, 250, 250, 125, 125, 100, 150)
)
obj <- alpha_adaptive_tree_pruned(node_dat = nd, delta_hat = 0.5)
# obj$alphafn — pass to find_blocks
# obj$update(pruned_nd, 0.05) — recompute on surviving tree
# obj$reset(0.05) — restore full-tree schedule